Application of the Generalized Decomposition Method for Solving the Nonlinear Problem of Jeffery–Hamel Flow

Abstract

In this paper the nonlinear problem of the two-dimensional flow of an incompressible viscous fluid between nonparallel plane walls is investigated analytically. The third-order nonlinear differential equation governing the dynamic field of the considered flow has been treated by a new analytical method called the generalized decomposition method (GDM). Indeed, this method introduces a new strategy of decomposition that can use all necessary information concerning the terms of series solutions and the nonlinear term Nu. This paper investigates, on the one hand, the velocity distribution in convergent and divergent channels for various Reynolds numbers, Re and various channel half-angles, ?, and, on the other hand, the compares our results with the results obtained by the fourth-order Runge Kutta method and other applied analytical methods, thus showing the higher accuracy of the adopted generalized decomposition method.